141 citations · 790 across the 75 of their papers we have counts for
7 papers · 2 filters
Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions
Guy David, Svitlana Mayboroda
The present paper establishes equivalence between uniform rectifiability of the boundary of a domain and the property that the Green function for elliptic operators is well approxi…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of w…
Carleson perturbations of elliptic operators on domains with low dimensional boundaries
Svitlana Mayboroda, Bruno Poggi
We prove an analogue of a perturbation result for the Dirichlet problem of divergence form elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators…
Good elliptic operators on Cantor sets
Guy David, Svitlana Mayboroda
It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that no…
Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets
G. David, S. Mayboroda
It was recently shown that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a domain with an dimensional uniformly rectifiable boundary,…
Elliptic theory in domains with boundaries of mixed dimension
Guy David, Joseph Feneuil, Svitlana Mayboroda
Take an open domain whose boundary may be composed of pieces of different dimensions. For instance, can be a ball on , minus one of its diam…